neighbor-cell assisted error correction for mlc nand flash
TRANSCRIPT
Neighbor-Cell Assisted Error Correction
for MLC NAND Flash Memories
Yu Cai1 Gulay Yalcin2 Onur Mutlu1 Erich F. Haratsch3
Adrian Cristal2 Osman S. Unsal2 Ken Mai1
1 Carnegie Mellon University 2 Barcelona Supercomputing Center 3 LSI Corporation
Executive Summary Problem: Cell-to-cell Program interference causes threshold voltage of flash cells to
be distorted even they are originally programmed correctly
Our Goal: Develop techniques to overcome cell-to-cell program interference
Analyze the threshold voltage distributions of flash cells conditionally upon the values of immediately neighboring cells
Devise new error correction mechanisms that can take advantage of the values of neighboring cells to reduce error rates over conventional ECC
Observations: Wide overall distribution can be decoupled into multiple narrower conditional distributions which can be separate easily
Solution: Neighbor-cell Assisted Correction (NAC)
Re-read a flash memory page that initially failed ECC with a set of read reference voltages corresponding to the conditional threshold voltage distribution
Use the re-read values to correct the cells that have neighbors with that value
Prioritize reading assuming neighbor cell values that cause largest or smallest cell-to-cell interference to allow ECC correct errors with less re-reads
Results: NAC improves flash memory lifetime by 39%
Within nominal lifetime: no performance degradation
In extended lifetime: less than 5% performance degradation
2
Outline
Background of Program Interference in NAND Flash Memory
Statistical Analysis of Cell-to-cell Program Interference
Neighbor-cell Assisted Correction (NAC)
Evaluation
Conclusions
3
Flash challenges: Reliability and Endurance
E. Grochowski et al., “Future technology challenges for NAND flash and HDD products”,
Flash Memory Summit 2012
P/E cycles (required)
P/E cycles (provided)
A few thousand
Writing
the full capacity
of the drive
10 times per day
for 5 years
(STEC)
> 50k P/E cycles
4
NAND Flash Error Model
Noisy NAND Write Read
Dominant errors in NAND flash memory
Neighbor page program
Retention Erase block
Program page
Write Read
Cai et al., “Threshold voltage
distribution in MLC NAND Flash
Memory: Characterization, Analysis,
and Modeling”, DATE 2013
Cai et al., “Flash Correct-and-Refresh:
Retention-aware error management for
increased flash memory lifetime”, ICCD 2012
5
Cai et al., “Program Interference in
MLC NAND Flash Memory:
Characterization, Modeling, and
Mitigation”, ICCD 2013
Solutions?
How Aggressor Cells are Programmed
Programming 2-bit MLC NAND flash memory in two steps
6
Vth
ER
(11)
LSB
Program
Vth
ER
(11)
Temp
(0x)
MSB
Program
Vth
ER
(11) P1
(10)
P2
(00)
P3
(01)
1
1 1
0
0 0
How Program Interference Happens
Model of victim cell threshold voltage changes when neighbor cells are programmed
Victim
Cell
WL<0>
WL<1>
WL<2>
(n,j)
(n+1,j-1) (n+1,j) (n+1,j+1)
LSB:0
LSB:1
MSB:2
LSB:3
MSB:4
MSB:6
(n-1,j-1) (n-1,j) (n-1,j+1)
∆Vx ∆Vx
∆Vy ∆Vxy ∆Vxy
∆Vxy ∆Vxy ∆Vy
7
Kj
Kjy
Mn
nx
before
victimneighborvictim jnVyxVyxjnV1
0 ),(),(),(),(
Cai et al., “Program Interference in MLC NAND Flash Memory: Characterization, Modeling, and Mitigation”, ICCD 2013
Our Goals and Related Work Our goals
Analyze the threshold voltage distributions of flash cells conditionally upon the values of immediately neighboring cells
Devise new error correction mechanisms that can take advantage of the values of neighboring cells to reduce error rates over conventional ECC
Limitations of previous work Program interference mitigation [Cai+ICCD 2013]
Predict optimum read reference voltage for overall distribution (Unaware of the value dependence of neighbor aggressor cells)
Signal processing [Dong + TCAS-I 2010]
Assumes threshold voltage changes of neighbor aggressor cells are known (difficult to record)
Assume the average of threshold voltage of cells in erased state are known (not known for state-of-art flash memory)
Assume the threshold voltage of cells in the same state are close enough (greatly different)
Read the victim cells and neighbor aggressor cells with 2n times, where n is in the range of 4 and 6 (large latency)
8
Outline
Background of Program Interference in NAND Flash Memory
Statistical Analysis of Cell-to-cell Program Interference
Neighbor-cell Assisted Correction (NAC)
Evaluation
Conclusions
9
Flash Voltage Distribution Analysis
Formal statistically analyze
How to optimize read reference voltage?
What determines minimum raw bit error rate?
Overall distribution vs conditional distribution
Can we achieve smaller BER than minimum raw BER of overall distribution?
Empirical silicon measurement and validation
10
Optimizing Read Reference Voltage
Raw bit error rate (BER)
Optimum read reference voltage that achieves the minimum raw BER is at the cross-point of neighbor distributions when random data are programmed
11
Vth
Vref Pi State Pi+1 State
f(x)
(μ1, σ1)
g(x)
(μ2, σ2)
v
vdxxgPdxxfP )()( 10totalErrRate
Vopt
BER with Read Reference Voltage
12
Vref
Pi State Pi+1 State
V’ref
Modeling the Minimum BER
Minimum raw BER can be further minimized by
Increasing distance between neighbor distributions (μ2-μ1)
Decreasing the standard deviation (σ)
13
Optimum Vref
Pi State Pi+1 State
f(x)
(μ1, σ1)
g(x)
(μ2, σ2)
When
1. f(x) and g(x) are Gaussian
2. σ1 = σ2 = σ
dxxRBER
2/)12(
2 )2/exp(2
1min
dxxxQx
)2/exp(2
1)( 2
2/)12( x
Secrets of Threshold Voltage Distributions
14
……
…… Victim WL
Aggressor WL 11 10 01 00 01 10 11 00
N11 N11 N00 N00 N10 N10 N01 N01
State P(i) State P(i+1) Victim WL before MSB
page of aggressor WL
are programmed
State P’(i) State P’(i+1)
Victim WL after MSB
page of aggressor WL
are programmed
Overall vs Conditional Distributions (1)
Overall distribution: p(x)
Conditional distribution: p(x, z=m)
m could be 11, 00, 10 and 01 for 2-bit MLC all-bit-line flash
Overall distribution is the sum of all conditional distribution
15
N11 N11 N00 N00 N10 N10 N01 N01
State P’(i) State P’(i+1)
n
mmzxpxp
2
1),()(
Vth
Overall vs Conditional Distributions (2)
Distance of two neighbor overall distribution is the average of the distances of neighbor conditional distributions
Distance of conditional distribution of different type is close
Average interference is same when aggressor cells are programmed with the same value
Distance of two neighbor overall distribution is close to the distances of any neighbor conditional distributions
16
N11 N11 N00 N00 N10 N10 N01 N01
State P’(i) State P’(i+1)
Vth
))()((1
)(1
)(1
)()( )()1()()1()()1( iP
m
iP
m
iP
m
iP
m
iPiP xExEN
xEN
xEN
XEXE
Overall vs Conditional Distributions (3)
Variance of overall distribution is larger than the average of the variance of all conditional distributions
Different conditional distributions do not overlap
Variances of conditional distribution of different type are close
Variance of overall distribution is larger than that of any conditional distributions
17
N11 N11 N00 N00 N10 N10 N01 N01
State P’(i) State P’(i+1)
2
2))()((
1)(
1)( nmm xExE
NxVar
NXVar
Variance of
overall distribution
Variance of
conditional distribution
Distance of conditional
distribution pair
Vth
Overall vs Conditional Reading
Distance of two neighbor overall distribution is close to the distances of any neighbor conditional distributions
Variance of overall distribution is larger than that of any conditional distributions
Minimum raw BER when read with overall distribution will be larger than that when read with conditional distribution
18
N11 N11 N01 N01
State P’(i) State P’(i+1)
N00 N00 N10 N10 REFx
Vth
Hardware Platform for Measurement
19
Cai et al., “FPGA-based solid-state drive prototyping platform”, FCCM 2011
Cai et al., “Error patterns in MLC NAND flash memory: Measurement, characterization, and analysis”, DATE 2012
Measurement Results
20
P1 State P2 State P3 State
Raw BER of conditional reading is much smaller than overall reading
Large margin
Small margin
Summary
There exists an optimum read reference that can achieve the minimum raw BER
The minimum raw BER decreases as signal-to-noise ratio increases
The distance (signal) of the overall distribution between neighboring states is close to that of each of the conditional distributions
The variance (noise) of each conditional distribution is smaller than that of the overall distribution
The variances of different conditional distributions are close
The signal-to-noise ratio of the conditional distribution is larger than that of the overall distribution
The minimum raw BER obtained after reading with the conditional distribution is much smaller than that obtained after reading with the overall distribution.
21
Outline
Background of Program Interference in NAND Flash Memory
Statistical Analysis of Cell-to-cell Program Interference
Neighbor-cell Assisted Correction (NAC)
Evaluation
Conclusions
22
Neighbor Assisted Reading (NAR)
Neighbor assisted reading
Read neighbor pages and classifie the cells in a wordline into N types based on the values stored in the corresponding direct-neighbor aggressor cells (N=4 for 2-bit MLC flash)
Read the cells of each type, a different set of local optimum read reference voltages (that minimizes the bit error rate) is used (i.e., REFx11, REFx00, REFx10, REFx01)
Combined all reads as one complete read and send to ECC
Performance degradation
log2(N) neighbor reads plus N reads on the selected wordline
Down to 16.7% performance for 2-bit MLC flash memory
23
Neighbor Assisted Correction (NAC)
NAC is build upon NAR, but only triggered when optimum reading based on overall distribution fails
Performance degraded to
24
1
(1+Pfail (N+log2(N))) (Pfail <0.01)
How to select next local
optimum read reference
voltage?
Prioritized NAC
Dominant errors are caused by the overlap of lower state interfered by high neighbor interference and the higher state interfered by low neighbor interference
25
P(i)low P(i)
High P(i+1)low P(i+1)
High
P’(i)low P’(i)
High P’(i+1)low P’(i+1)
High
REFx REFx11 REFx01
State P(i) State P(i+1)
N11 N00 N10 N01
REFx00 REFx10
N11 N00 N10 N01
State P’(i) State P’(i+1)
Procedure of NAC
Online learning
Periodically (e.g., every 100 P/E cycles) measure and learn the overall and conditional threshold voltage distribution statistics (e.g. mean, standard deviation and corresponding optimum read reference voltage)
NAC procedure
Step 1: Once ECC fails reading with overall distribution, load the failed data and corresponding neighbor LSB/MSB data into NAC
Step 2: Read the failed page with the local optimum read reference voltage for cells with neighbor programmed as 11
Step 3: Fix the value for cells with neighbor 11 in step 1
Step 4: Send fixed data for ECC correction. If succeed, exit. Otherwise, go to step 2 and try to read with the local optimum read reference voltage 10, 01 and 00 respectively
26
Microarchitecture of NAC (Initialization)
……
……
……
……
……
Neighbor LSB Page
Buffer
Neighbor MSB Page
Buffer
Page-to-be-Corrected
Buffer
Local-Optimum-Read
Buffer
Bit1
Bit2
Comparator Vector
Pass Circuit Vector
1 0 1 0 1 0 1 1 0 1
1 0 0 1 0 1 0 1 1 1
0 1 0 0 1 0 1 0 1 1
Comp Comp Comp Comp Comp Comp Comp Comp Comp Comp
NAC (Fixing cells with neighbor 11)
……
……
……
……
……
Neighbor LSB Page
Buffer
Neighbor MSB Page
Buffer
Page-to-be-Corrected
Buffer
Local-Optimum-Read
Buffer
Bit1
Bit2
Comparator Vector
Pass Circuit Vector
1 0 1 0 1 0 1 1 0 1
1 0 0 1 0 1 0 1 1 1
0 1 0 0 1 0 1 0 1 1
Comp Comp Comp Comp Comp Comp Comp Comp Comp Comp
1 1
0 1 0 1 1 0 0 1 1 0
ON ON
0 1
Outline
Background of Program Interference in NAND Flash Memory
Statistical Analysis of Cell-to-cell Program Interference
Neighbor-cell Assisted Correction (NAC)
Evaluation
Conclusions
29
Lifetime Extension with NAC
30
ECC needs to correct
40 bits per 1k-Byte
Stage-1 Stage-2 Stage-3
39%
33%
22%
Stage-0
Performance Analysis of NAC
31
Conclusion
Provide a detailed statistical and experimental analysis of threshold voltage distributions of flash memory cells conditional upon the immediate-neighbor cell values
Observation: conditional distributions can be used to determine read reference voltages that can minimize raw bit error rate (RBER) when the cells are read
Neighbor-cell assisted error correction (NAC) techniques extend flash lifetime with negligible overhead
First read with global optimum read reference voltage
Correct the failed data with conditional reading
Conditional reading can be executed in prioritized order
Lifetime extend by 39% with negligible overhead
32
Thank You.
Neighbor-Cell Assisted Error Correction
for MLC NAND Flash Memories
Yu Cai1 Gulay Yalcin2 Onur Mutlu1 Erich F. Haratsch3
Adrian Cristal2 Osman S. Unsal2 Ken Mai1
1 Carnegie Mellon University 2 Barcelona Supercomputing Center 3 LSI Corporation